Algebra problem (40)


Problem

Solve x in:
(base of logarithm is 10)



Solution

Take log:



If y = log(x) then x = 10y



"Nice" answer, no approximations but help of a pocket calculator.
The solutions however are almost directly visible in the original equation.
This suggests that the equation can be solved without calculator.

There we go.
Keep in mind that



and the root may be rewritten as:



which converts the equation to



with the same answers.